SMK Raja Perempuan, Ipoh
SCHEME OF WORK
2011
ADDITIONAL MATHEMATICS
FORM 5
YEARLY TEACHING PLAN FOR ADDITIONAL MATHEMATICS FORM 5
2011
WeekS/DATE / Learning Objectives
Students will be taught to… / Learning Outcomes
Students will be able to… / Suggested teaching and learning activities / Values AND POINTS TO NOTE / Teaching Aids / CCTS
1
(3.1.11 -7.1.11)
2
(10.1.11 –
14.1.11)
3
(17.1.11-21.1.11) / ALGEBRAIC COMPONENT
a6: progression
1. Understand and use the concept of arithmetic progression.
2. Understand and use the concept
of geometric progression / Level 1
1.1Identify characteristics of arithmetic progressions.
1.2Determine whether given sequence is an arithmetic progression.
Level 2
1.3Determine by using formula:
a)specific terms in arithmetic progressions;
b)the number of terms in arithmetic progressions
1.4Find :
a)the sum of the first n terms of arithmetic progressions.
b)the sum of a specific number of consecutive terms of arithmetic progressions
c)the value of n, given the sum of the first n terms of arithmetic progressions
Level 3
1.5Solve problems involving arithmetic progressions.
Level 1
2.1 Identify characteristics of
geometric progressions
2.2 Determine whether a
given sequence is a
geometric progression.
Level 2
2.3 Determine by using
formula
a)specific terms in geometric progressions
b) the number of terms in
geometric progressions
2.4 Find :
a) the sum of the first n terms of
geometric progressions
b)the sum of a specificnumber of consecutive terms of geometric
progressions.
Level 3
2.5 Find :
a) the sum to infinity of
geometric progressions
b) the first term or common
ratio, given the sum to
infinity of geometric
progressions.
2.6 Solve problems involving
geometric progressions. / Use example from real-life situations, scientific or graphing calculator software to explore arithmetic progressions.
Use examples from real-life situations, scientific or graphing calculators ; and computer software to explore geometric progressions / Systematic
Careful, hardworking, confidence
Begin with sequences to introduce arithmetical and geometrical progressions.
Include examples in algebraic form.
Include the use of the formula Tn= Sn - Sn-1
Include problems involving real-life situations
Discuss :
As n →, rn →0 then S
S read as “sum to infinity”.
Include recurring decimals. Limit to 2 recurring digits such as 0., 0.,…
Exclude :
a)combination of arithmetic progressions and geometric progressions.
b)Cumulative sequences such as, (1), (2,3), (4,5,6), (7,8,9,10),….. / Coloured blocks, whiteboard, text book, chards, scientific calculator, work sheet, list of formulae.
Interpreting, Identifying relations, Making Inference, Translating,
Using of ICT, Problem solving, Mathematical communication
Construction
Problem-solving
Graph board, geometric sketchpad, calculator, teaching courseware.
Identifying relationship, working out mentally, comparing and contrasting, finding all possible solutions,
arranging in.
Characterizing,
identify patterns
evaluating.
Problem-solving
4
(24.1.11-
28.1.11) / ALGEBRAIC COMPONENT
a7: LINEAR LAW
1. Understand and use the concept of lines of best fit.
2. Apply linear law to non-linear relations. / Level 1
1.6Draw lines of best fit by inspection of given data.
Level 2
1.7Write equations for lines of best fit.
1.8Determine values of variables from:
a)lines of best fit
b)equations of lines of best fit.
Level 3
2.1Reduce non-linear relations to linear form.
2.2Determine values of constants of non-linear relations given:
a)lines of best fit
b)data.
2.3Obtain information from:
a)lines of best fit
b)equations of lines of best fit. / Use examplesfrom real-life situations to introduce the concept of linear law.
Use graphing calculators or computer software such as Geometer’s Sketchpad to explore lines of best fit. / Patience
Accuracy
Neatness
Limit data to linear relations between two variables. / Whiteboard, text book, graph board, scientific calculator, graph papers, long ruler,
Geometer Sketchpad,
Teaching Courseware.
Identify patterns, Comparing and contrasting,
Conceptualizing Translating, Construction, Interpreting, Predicting.
5
(31.1.11-4.2.11) / CHINESE NEW YEAR
6
(7.2.11-
11.2.11) / CALCULUS COMPONENT
C2: INTEGRATION
- Understand and use the concept of indefinite integral.
1.1Determine integrals by reversing differentiation.
1.2Determine integrals of ax n, where a is a constant and n is an integer, n≠1.
1.3Determine integrals of algebraic expressions.
1.4Find constants of integration, c, in indefinite integrals.
Level 2
1.5Determine equations of curves from functions of gradients.
1.6Determine by substitution the integrals of expressions of the form (ax + b) n, where a and b are constants, n is an integer n≠1. / Use computer software such as Geometer’s Sketchpad to explore the concept of integration. / Patience ,
co-operation, rational, systematic and diligence.
Cooperation.
Emphasize constant of integration.
read as ‘integration of y with respect to x”
Limit integration of
w here
u = ax + b. / Text Book
White board
Roll-up board
Scientific calculator
Conceptual map
List of integration formula.
Graphic calculator.
Simulation and use of ICT.
Problem solving
Communication in mathematics.
Contextual Learning
Constructivism Learning.
Cooperative Learning.
Mastery Learning.
Self-Access Learning.
Logical Reasoning.
7
(14.2.11-
18.2.11) / PRE USBF 1
8
(21.2.11
25.2.11) / C2: INTERGRATION
- Understand and use the concept of definite integral.
2.1Find definite integrals of algebraic expressions.
Level 3
2.2Find areas under curves as the limit of a sum of areas.
2.3Determine areas under curves using formula. / Use scientific or graphic calculators to explore the concept of definite integrals.
Use computer software and graphic calculators to explore areas under curves and the significance of positive and negative values of areas. / Include
Derivation of formulae not required.
Limit to one curve. / CCTS:
Identifying relationships.
Working out mentally.
Evaluating.
Visualizing
Analyzing
Drawing diagrams
Arranging in order.
Making conclusions.
9
(28.2.11-
4.3.11) / USBF 1
10
(7.3.11-11.3.11) / C2: INTERGRATION / 2.4Find volume of revolutions when
region bounded by a curve is
rotated completely about the
(a)x-axis,
(b)y-axis.
2.5 As the limit of a sum of volumes.
Determine volumes of revolutions
using formula. / Use dynamic computer software to explore volumes of revolutions. / Limit volumes of revolution about thex-axis or
y-axis.
MID TERM BREAK
(12.3.2011 – 20.3.2011)
11
(21.3.11-25.3.11)
12
(28.3.11-
1.4.11) / GEOMETRIC COMPONENT
G2: VECTORS
1. Understand and use the concept of vector.
2. Understand and use the
concepts of addition and
subtraction of vectors. / Level 1
1.1 Differentiate between vector and scalar quantities.
1.2 Draw and label directed line segments to represent vectors.
1.3 Determine the magnitude and direction of vectors represented
by directed line.
1.4 Determine whether two vectors are equal.
Level 2
1.5 Multiply vectors by scalars.
1.6 Determine whether two vectors
are parallel.
Level 1
2.1Determine the resultant vector of two parallel vectors.
Level 2
2.2Determine the resultant vector of two non-parallel vectors using :
(a)triangle law
(b)parallelogram law.
2.3Determine the resultant vector of three or more vectors using the polygon law.
Level 3
2.4Subtract two vectors which are :
(a)parallel
(b)non-parallel
2.5Represent vectors as a combination of other vectors.
2.6Solve problems involving addition and subtraction vectors. / Use example from real-life situations and dynamic computer software such as Geometer’s Sketchpad to explore vectors.
Use real-life situations and manipulative materials to explore addition and subtraction of vectors. / Patience ,
co-operation, rational, systematic and diligence.
Use notations:
Vectors : , a, AB.
Magnitude :
.
Zero vector: .
Emphasise that a zero vector has magnitude of zero.
Emphasize negative vector:
Include negative scalar.
Include :
(a) collinear
points
(b) non-parallel
non-zero
vectors.
Emphasize :
If and are not parallel and h = k, then h = k = 0.
Emphasize :
-=
+(-) / whiteboard, text book, chards, scientific calculator, work sheet, list of formulae,
Cartesian plane,
Using CD courseware
Interpreting, Identifying vectors, Making Inference,
Using of ICT,
Problem solving, Mathematical communication
Interpreting, Identifying relations, Making Inference, Translating,
Comparing and
contrasting
13
(4.4.11-8.4.11) / 3. Understand and use vectors in
the Cartesian plane. / Level 1
3.1Express vectors in the form:
a)
b)
3.2Determine magnitudes of vectors.
Level 2
3.3Determine unit vectors in given directions.
3.4Add two or more vectors.
3.5Subtract two vectors.
3.6Multiply vectors by scalars.
Level 3
3.7Perform combined operations in vectors.
3.8Solve problems involving vectors. / Use example from real-life situations, computer software to explore vectors in the Cartesian plane. / Relate unit vectors and to Cartesian coordinates.
Emphasise:
vector = and
vector =
For learning outcomes 3.2 to 3.7, all vectors are given in the form
or .
Limit combined operations to addition, subtraction and multiplication of vectors by scalars. / Whiteboard, colour chalks, text book, chards, scientific calculator, work sheet,
grid board.
Using of ICT, Problem solving, Mathematical
communication
14
(11.4.11-
15.4.11) / TRIGONOMETRIC component
t2: trigonometric functions
1. Understand the concept of positive and negative angles measured in degrees and radians.
2. Understand and use the six
trigonometric functions of
any angle / Level 1
1.1 Represent in a Cartesian plane, angles greater than 360 or 2л radians for:
a)positive angles
b)negative angles
2.1Define sine, cosine and tangent of any angle in a Cartesian plane.
2.2Define cotangent, secant and
Cosecant of any angle in a Cartesian plane
2.3Find values of the six
Trigonometric functions of any
angle.
2.4 Solve trigonometric equations / Use dynamic computer software such as Geometer’s Sketchpad to explore angles in Cartesian plane.
Use dynamic computer software to explore trigonometric functions in degrees and radians
Use scientific or graphic calculators to explore trigonometric functions of any angle. / Confidence
Patience
Careful
Use unit circle to determine the sine of trigonometric ratios.
Emphasise:
sin = cos (90 - )
cos = sin (90 - )
tan = cot(90 - )
cosec = sec (90 - )
sec =cosec(90-)
cot = tan(90 - )
Emphasise the use of triangles to find trigonometric ratios for special angles 30, 45 and 60. / list of formulae,
computer software,
graphic calculators
15
(18.4.11-
22.4.11) / PRE MID-YEAR EXAMINATION
16
(25.4.11-
29.4.11)
17
(2.5.11-6.5.11) / 3. Understand and use graphs of
sinus , cosines and tangent
functions.
4. Understand and use basic identities
5. Understand and use addition formulae and double-angle formulae. / Level 2
3.1 Draw and sketch graphs of
trigonometric functions :
(a) y = c + a sin bx
(b) y = c + a cos bx
(c) y = c + a tan bx
where a, b and c are constants
and b > 0.
Level 2
3.2 Determine the number of
solutions to a trigonometric
equation using sketched graphs.
3.3 Solve trigonometric equations
using drawn graphs.
Level 3
4.1Prove basic identities :
c)
d)
e)
4.2Prove trigonometric identities using basic identities.
4.3Solve trigonometric equation using basic identities
Level 3
5.1 Prove trigonometric identities using addition formulae for and .
5.2 Derive double-angle formulae for , and .
5.3 Prove trigonometric identities using addition formulae and/or double-angle formulae.
5.4 Solve trigonometric equations. / Use examplesfrom real-life situations to introduce graphs of trigonometric functions.
Use graphing calculators and dynamic computer software such as Geometer’s Sketchpad to explore graphs of trigonometric functions.
Use scientific or graphing calculators and dynamics computer software such as Geometer’s Sketchpad to explore basic identities.
Use dynamic computer software such as Geometer’s Sketchpad to explore
addition formulae and double-angle formulae. / Use angles in
(a) degrees
(b) radians,
in terms
of ח .
Emphasise the characteristics of sine, cosine and tangent graphs. Include trigonometric functions involving modulus.
Exclude combinations of trigonometric functions.
Basic identities are also known as Pythagorean identities
Include learning outcomes 2.1 and 2.2.
Derivation of addition formulae not required.
Discuss half-angle
formulae.
Exclude :
+, / Coloured blocks, whiteboard, text book, scientific calculator, work sheet, list of formulae.
Interpreting, Identifying relations, Making Inference, Translating,
Using of ICT, Problem
solving, Mathematical communication
18 -19
(9.5.11-20.5.11) / MID YEAR EXAMINATION
20
(23.5.11-
27.5.11) / STATISTICS COMPONENT
S2: pERMUTATIONS AND COMBINATION
1. Understand and use the concept of permutation. / Level 1
1.1 Determine the total number of ways to perform successive events using multiplication rule.
1.2 Determine the number of permutations of n different objects.
1.3 Determine the number of
permutation of n different
objects taken r at a time
Level 2
1.4 Determine the number of
permutations of n different
objects for given conditions.
1.5 Determine the number of
permutations of n different
objects f taken r at a time
for given conditions / Use manipulative materials to explore multiplication rule.
Use real-life situations and computer software to explore permutations / Predicting Critical thinking
Making inferences
Patience
For this topic:
a) Introduce the concept by using numerical examples.
b) Calculators should only be used after students have understood the concept.
Limit to 3 events
Exclude cases involving identical objects. / Teaching Courseware,
LCD,
Screen,
Computer.
whiteboard, text book, scientific calculator, work sheet, list of formulae
Interpreting, Identifying relations, Making Inference,
Using of ICT, Problem solving, Mathematical communication
MID YEAR BREAK
(28.5.2011 – 12.6.2011)
21
(13.6.11-
17.6.11) / S2: pERMUTATIONS AND COMBINATION
2. Understand and use the concept of combination / Level 1
2.1Determine the number of combinations of r objects chosen from n different objects.
Level 2
2.2Determine the number of combinations of r objects chosen from n different objects for given conditions. / Explore Combinations Using Real-Life Situations And Computer Software. / Explain the concept of permutations by listing all possible arrangements.
Include notations
a) n! = n(n-1)(n-2)…(3)(2)(1)
b) 0! =1
n! read as “n factorial”
Exclude cases involving arrangement of objects in a circle.
Explain the concept of combinations by listing all possible selections.
Use examples to illustrate = / Teaching Courseware,
LCD,
Screen,
Computer.
whiteboard, text book, scientific calculator, work sheet, list of formulae
Interpreting, Identifying relations, Making Inference,
Using of ICT, Problem solving, Mathematical communication
Coloured blocks, blackboard, text book, cards, scientific calculator,
Formulae sheet,
work sheet,
Making Inference, Predicting,
Using of ICT,
Analyzing
22
(20.6.11-24.6.11)
23
(27.6.11-1.7.11) / statistics component
s3: probability
- Understand and use the
2. Understand and use the concept of probability of mutually exclusive events.
3. Understand and use the concept of probability of independent events. / Level 1
1.1 Describe the sample space of an experiment.
1.2 Determine the number of outcomes of an event
1.3 Determine the probability of an event.
Level 2
1.4 Determine by using formula:
a) specific terms in arithmetic progressions;
b) the number of terms in arithmetic progressions.
Level 2
2.1Determine whether two events are
mutually exclusive.
2.2Determine the probability of two or more events that are mutually exclusive.
Level 3
3.2 Determine whether two events
are independent.
3.2 Determine the probability of
two independent events.
3.3 Determine the probability of
three independent events. / Use example from real-life situations, scientific or graphing calculator software to explore arithmetic progressions.
Use manipulative materials and graphing calculators to explore the concept of probability of mutually exclusive events.
Use computer software to simulate experiments involving probability of mutually exclusive events.
Use manipulative materials and graphing calculators to explore the concept of independent
events.
Use computer software to simulate experiments involving probability of independent events / confidence
Use set notations
Discuss:
a. Classical
probability (theoreticalprobability) cal progressions.
b. Subjective probability
c. relative frequency probability (experimental probability)
Emphasize:
Only classical probability is used to solve problems
Emphasize:
Using Venn Diagrams.
Include events that are mutually exclusive and exhaustive.
Limit to three mutually exclusive events.
Include tree diagrams. / Teaching Aids:
Dice, coins,
cards,
scientific calculator,
Computers,
Graphing calculators software.
Manipulative materials.
CCTS :
Identifying relationship,
Problem solving,
Identify Patterns,
Conceptualizing,
Making hypothesis.
Problem Solving.
Identifying relationship.
Grouping and classifying.
Predicting.
24
(4.7.11-8.7.11)
25
(11.7.11-15.7.11) / STATISTICS COMPONENT
S4 : PROBABILITY DISTRIBUTIONS
1. Understand and use the concept of binomial distribution.
- Understand and use the concept of normal distributions
1.1 List all possible values of a discrete random variable.
Level 2
1.2 Determine the probability of an event in a binomial distribution.
1.3 Plot binomial distributions graphs.
1.4 Determine mean, variance, and standard deviations of a binomial distributions
Level 3
1.5 Solve problems involving binomial distribution.
Level 1
2.1Describe continuous random variables using set notations.
2.2Find probability of z-values for standard normal distribution.
Level 2
2.3Convert random variable of normal distributions, X, to standardized variable, Z.
Level 3
2.4Represent probability of an event using set notation.
2.5Determine probability of an event.
Solve problems involving normal distributions. / Teacher needs to explain the definition of discrete random variable.
Discuss the characteristics of Bernoulli trials.
Students are not required to derive the formulae.
The cases should not include large values of n.
Mean = np
Variance = npq
Standard deviation =
n = number of trials
p = probability of success
q = probability of failure.
Use real-life situations and computer software such as statistical packages to explore the concept of normal distributions. / Honesty, fairness, careful, independent
Includes the characteristics of Bernoulli trials.
For learning outcomes 1.2 and 1.4, derivations of formulae not required.
Discuss characteristics of:
a)nnormal distribution graphs.
b)gStandard normal distribution graphs
Z is called standardized variable.
Rational and careful
Integration of normal distribution function to determine probability is not required / Courseware,
Workbook,
Textbooks,
GSP,
Calculator,
Log book,
Z-score table
Identifying relationship,
Estimating,
Evaluating,
Analyzing
Normal distribution table, scientific calculator, text book
Critical thinking, Interpreting, translating, identifying relationship, problem solving, drawing diagram .
26
(18.7.11-22.7.11) / science and technology package
AST2: Motion along a straight linE
1. Understand and use the concept of displacement. / Level 1
1.1 Identify direction of displacement of a particle from a fixed point.
1.2 Determine displacement of a particle from a fixed point.
Level 2
1.3Determine the total distance traveled by a particle over a time interval using graphical method. / Use real-life examples, scientific or graphing calculator and computer software such as Geometer’s Sketchpad to explore displacement. / cooperation
independent
confidence
Hardworking
Emphasize the use of the following symbols:
s=displacement
v=velocity
a=acceleration
t=time
where s, v and a are function of time.
Emphasize the difference between displacement and distance.
Discuss positive, negative and zero displacements.
Include the use of number line. / Scientific calculator, worksheet, list of formulae, using ICT, problem solving.
Working backwards, drawing diagram, analyzing, problem solving.
Whiteboard, text book, scientific
calculator, work sheet, list of formulae.
Using of ICT,
Problem solving, Mathematical communication
Interpreting, Identifying relations, Making Inference,
27
(25.7.11-29.7.11) / 2. Understand and use the concept of velocity.
3. Understand and use the concept of acceleration. / Level 2
2.1 Determine velocity function of a
particle by differentiation.
2.2 Determine instantaneous velocity
of a particle.
Level 3
2.3 Determine displacement of a
particle from velocity function by
integration
Level 2
3.1Determine acceleration function of a particle by differentiation.
Level 3
3.2Determine instantaneous acceleration of a particle.
3.3Determine instantaneous velocity of a particle from acceleration function by integration.
3.4Determine displacement of a particle from acceleration function by integration.
3.5Solve problems involving motion along a straight line. / Use real-life examples, graphing calculators and computer software such as Geometer’s Sketchpad to explore the concept of velocity.
Discuss about the idea of acceleration as the changing of the rate of velocity.
a = dv/dt , d2s /dt2
Discuss about the idea of uniform acceleration
Meaning of the signs of acceleration:
a 0 / The velocity of the particle is increasing with respect to time
a < 0 / The velocity of particle is decreasing with respect to time
a = 0 / The particle is at uniform velocity or maximum velocity
/ Emphasize velocity as the rate of change of displacement
v =
Include graphs of velocity functions
Discuss:
a) uniform
velocity
b) zero instantaneous
c) positive
velocity
d) negative
velocity
s =
Emphasis acceleration as the rate of
change of velocity.
Discuss :
a) uniform
acceleration
b) zero
acceleration
c) positive
acceleration
d) negative
acceleration
28
(1.8.11-5.8.11) / SPM Strategic revision
29 (8.8.11 - 12.8.11 ) / PRE TRIAL EXAMINATION
30 – 31 (15.8.11 - 26.8.11 ) / SPM Strategic revision
MID TERM BREAK & HARI RAYA AIDILFITRI
(27.8.2011 - 4.9.2011)
32
(5.9.11-9.9.11) / SPM Strategic revision
33 – 34
(12.9.11-23.9.11) / TRIAL EXAMINATION
35-41
(26.9.11-
11.11.11) / SPM STRATEGIC REVISION
SPM EXAMINATION
14.11.11– 14.12.11)
Prepared By: